Bel- this is a C&P from the Illinois State Police Website, FAQs on FOIDs-

I am under the age of 21, can I apply for a FOID card?
Yes. In addition to all other requirements, a person who is under 21 years of age must have the written consent of his or her parent or legal guardian to possess and acquire firearms and firearm ammunition. Also, he or she must not have been convicted of a misdemeanor other than a traffic offense or adjudged delinquent. The parent or legal guardian providing written consent must be eligible to possess a valid FOID card.

I am under the age of 21, do I need a FOID card?
Not necessarily. The FOID Act exempts unemancipated minors while in the custody and immediate control of their parent, legal guardian, or other person in loco parentis to the minor as long as their parent, legal guardian, or other person in loco parentis to the minor has a valid FOID card in their possession.

Will I be held responsible for my child who has access to a firearm?
Yes. Illinois law (720 ILCS 5/24-9) states "(a) Except as provided in subsection (c), it is unlawful for any person to store or leave, within premises under his or her control, a firearm if the person knows or has reason to believe that a minor under the age of 14 years who does not have a Firearm Owners Identification Card is likely to gain access to the firearm without the lawful permission of the minor's parent, guardian, or person having charge of the minor, and the minor causes death or great bodily harm with the firearm, unless the firearm is:
(1) secured by a device or mechanism, other than the firearm safety, designed to render a firearm temporarily inoperable; or
(2) placed in a securely locked box or container; or
(3) placed in some other location that a reasonable person would believe to be secure from a minor under the age of 14 years.
(b) Sentence. A person who violates this Section is guilty of a Class C misdemeanor and shall be fined not less than $1,000. A second or subsequent violation of this Section is a Class A misdemeanor.
(c) Subsection (a) does not apply:
(1) if the minor under 14 years of age gains access to a firearm and uses it in a lawful act of self-defense or defense of another; or
(2) to any firearm obtained by a minor under the age of 14 because of an unlawful entry of the premises by the minor or another person."